|By Kylie MacLellan and William James

|By Kylie MacLellan and William James

|By Kylie MacLellan and William James

LONDON (Reuters) - Britain will quit the EU single market when it leaves the European Union, Prime Minister Theresa May said on Tuesday in a decisive speech that set a course for a clean break with the world's largest trading bloc.

Setting out a vision that could determine Britain's future for generations and the shape of the EU itself, May answered criticism that she has been coy about her strategy with a 12-point plan for what has been dubbed a "hard Brexit".

May promised to seek the greatest possible access to European markets but said Britain would aim to establish its own free trade deals with countries far beyond Europe, and impose limits on immigration from the continent.

For the first time, she acknowledged that those measures would require withdrawing from the market of 500 million people, founded on principles of free movement of goods and people.

"I want to be clear: what I am proposing cannot mean membership of the single market," said May, who became prime minister in the turmoil after Britain voted in June to leave the EU. "Instead, we seek the greatest possible access to it through a new comprehensive, bold and ambitious free trade agreement."

The media had been briefed on some of the points in May's speech since Sunday, and the expectation she would signal a hard Brexit had caused the pound to fall on currency markets from the start of this week.

Markets rallied during the speech itself, however, especially when she announced that parliament would be given a vote on the final terms of Britain's exit, seen as a steadying influence. Sterling rose 2.9 percent against the dollar on the day, the biggest rally in a single day since at least 1998.

"WHERE IS THE GIVE?"

The Brexit talks are expected to be one of the most complicated negotiations in post-World War Two European history, and the view in Brussels is that her goal of wrapping up a trade deal in two years is ambitious.

There was a lukewarm reception to May's speech from some political leaders in EU countries, highlighting the arduous task ahead.

"Where is the give for all the take?" asked the Czech Republic's secretary of state for EU affairs, Tomas Prouza, on Twitter, while EU Council President Donald Tusk lamented what he called a "sad process, surrealistic times".

However, Germany's foreign and economy ministers were among many who welcomed the greater clarity provided by the speech after months of guesswork on the continent as to Britain's intentions.

May's task will be further complicated by dissent within the United Kingdom, notably in Scotland, where a majority voted to remain in the EU. First Minister Nicola Sturgeon has raised the prospect of a new referendum on independence from Britain, which Scottish voters rejected in 2014.

"The UK government cannot be allowed to take us out of the EU and the single market, regardless of the impact on our economy, jobs, living standards ... without Scotland having the ability to choose between that and a different future," said Sturgeon after May's speech.

May campaigned to remain in the EU before last June's vote, but since taking over from David Cameron, who quit following his referendum defeat, she has backed the decision to leave.

She said in her speech she would not adopt models used by other countries that have free trade agreements with the EU. Norway, for example, is outside the bloc but a member of the wider European Economic Area, giving it access to the single market while subjecting it to many EU rules.

May said her negotiating priorities included limiting immigration, leaving the jurisdiction of the European Court of Justice, and ending full membership of the customs union that sets external tariffs for goods imported into the bloc.

Full membership of the customs union prevented Britain making its own trade deals, May said, but she still wanted a deal to keep trade with Europe as "frictionless as possible".

Britain's financial industry, which accounts for about 10 percent of the economy, is now expected to push ahead with plans to relocate parts of businesses elsewhere in the EU so they can continue to sell their services across the bloc.

Britain's overwhelmingly foreign-owned car sector was quick to react, warning through industry body SMMT that participation in the customs union was vital to help retain trade, while Germany's BMW also said "uncomplicated, tariff-free access" to the single market was essential.

"NO DEAL BETTER THAN BAD DEAL"

London will trigger the formal Brexit talks by the end of March, ushering in a two-year period of talks. May said she wanted the terms of Britain's exit to be agreed within those two years, with new rules implemented gradually where necessary.

"It is in no one's interests for there to be a cliff edge for business or a threat to stability," May said. "We will do everything we can to phase in the new arrangements we require."

But she also set a firm tone for the negotiations, saying: "No deal for Britain is better than a bad deal for Britain."

She hinted that Britain could use tax breaks to fight back to keep businesses if the EU insisted on punitive tariffs.

Just as May was setting out her pitch, her finance minister Philip Hammond told parliament Britain could get tough if a comprehensive trade agreement with the EU was not forthcoming.

"If we don't (get a sensible Brexit deal), the people of this country are not simply going to lie down and accept that we will be poorer," he said. "We will do whatever it takes to maintain our competitiveness and protect our standard of living."

May's speech also comes as Northern Ireland, part of the UK most exposed to Brexit due to its land border with the Republic of Ireland, faces political paralysis after a government that shared power between Catholics and Protestants collapsed.

One of May's principles was "strengthening the union", she said in a nod to both Northern Ireland and Scotland.

But Gerry Adams, president of the Sinn Fein party which was part of the power-sharing government in the north and is a growing force in the Republic of Ireland, said it was hard to see how May's Brexit plan could work without significant changes to the border arrangements between north and south.

U.S. President-elect Donald Trump has said that Brexit will turn out to be a great thing and other countries would follow Britain out of the European Union. He promised to strike a swift bilateral trade deal with the United Kingdom.

May said she did not want the EU to unravel.

"It would not be in the best interest of Britain. It remains overwhelmingly and compellingly in Britain's best national interest for the EU to succeed," she said.